This invention relates to a power meter for accurately measuring voltage across and current through a load using a voltage sensor and a differentiating current sensor, i.e. a current sensor which outputs a signal representing the derivative with respect to time of the current measured.
U.S. Patent No. 5,243,536, co-owned with the present application, teaches how to use a voltage sensor which outputs a v(t) signal and a current sensor which outputs an i(t) signal to provide a measurement of voltage, volt.sup.2 -hours (an integration of v.sup.2 (t) over time), current, amp.sup.2 -hours (an integration of i.sup.2 (t) over time), watts (v(t).times.i(t)), VAR-hours (volt-amps reactive--(quadrature v(t)).times.i(t)), and similar quantities related to electrical parameters of the load. The term v(t) is, at various times, referred to as the voltage as a function of time, the instantaneous voltage at time t, or the voltage waveform, while the term i(t) is referred to as the current as a function of time, the instantaneous current at time t, or the current waveform. Herein, the derivative of i(t), shown as d[I(t)]/dt or just di/dt, refers to the time derivative of the current signal, also known as the differentiation of the current signal. For clarity, the analog functions are referred to herein as signals, and the digitized versions of these signals are referred to herein as sample streams, or waveforms.
Each of these parameters can be derived from v(t) and/or i(t). In the apparatus shown in U.S. Pat. No. 5,243,536, these two signals are converted to digital sample streams, which are then manipulated by digital circuits to find the desired electrical parameters, such as instantaneous power, average power, or total energy (usually measured in watt-hours or kilowatt-hours) consumed by the load.
The accurate measurement of these parameters finds many applications, one of which is in the field of utility service metering, where the load under measurement might be a residence, business, or factory. In the design of power meters, accuracy and cost are important. If errors in the readings of the v(t) and i(t) signals result in too high a reading, customers will object, and if the errors result in too low a reading, the utility will lose revenue. A utility meter must also be inexpensive, because the utility must provide at least one meter to each of their customers.
The voltage signal v(t) is sometimes measured using an operational amplifier (op-amp), possibly with the addition of a resistive divider network spanning two points of the load, while the current signal i(t) is sometimes measured by placing a small resistor in line with a conductor carrying the current. The voltage developed across the small resistor would then provide a voltage proportional to the current in the load. After multiplying by a suitable factor, i(t) is derived from this voltage.
Several problems arise with using a resistor to measure the current. In large loads, the power loss through the resistor is significant. Also, the resistor's temperature coefficient will cause its resistance to vary over temperature, thus causing variations in the measured i(t) signal for a steady current. These problems can be avoided through the use of a differentiating current sensor, which provides a differentiated current signal, d[i(t)]/dt, instead of i(t).
A differentiating current sensor might be provided by an inductive coil magnetically coupled to a conductor carrying the current to be measured. Since the voltage induced in an inductor is L.times.(di/dt), the inductor provides the differentiated current signal as a voltage, which is integrated to find i(t). Differentiating current sensors introduce a new set of problems however, in that the di/dt signal must be integrated. Even if the manipulation of v(t) and i(t) is performed digitally, the integration of i(t) is typically done with analog circuits because the stability of an analog integrator has been more easy to achieve than the stability of a digital integrator. However, an analog integrator requires analog components: at least one resistor and one capacitor per current channel, and these analog components have values which are temperature dependent and which drift over time. Using stable analog components is costly, and even then it does not remove all the temperature and time dependence.
A digital integrator creates several difficulties, however. One problem is the introduction of a phase shift of slightly less than -90.degree. which does not totally compensate for the phase shift of exactly 90.degree. caused by the differentiation done by the current sensor. This synchronization of the current and voltage signals is important, so that v(t) and i(t) values for a given t are easily multiplied when calculating power values. An analog integrator does not have this problem, since the phase shift of an analog integrator can be made to be exactly -90.degree.. Of course, the difference between the phase shift of an analog integrator and a digital integrator is reduced as the sampling rate of the integrator increases, but it is never zero for finite sampling rates.
Therefore, what is needed is a current measuring device which can measure the current and output i(t) without a phase shift relative to v(t), and still do it inexpensively and with a minimum of temperature dependence.